1. POLYHEDRON

2. What do these have in common?
These are all polygons!

3. What do these have in common?
These are not polygons!

4. What do these have in common?
These are 3-D!

5. These are NOT polyhedron:

6. What is a polyhedron? These are polyhedron: Click here for
more polyhedron
Crystallographic
polyhedra
Create your own
polyhedron
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more polyhedron

7. A polyhedron is: -three dimensional; -a closed figure;
-made up of flat surfaces which are polygons.
What is a polyhedron?
A polyhedron is a three-dimensional solid whose faces are polygons joined at their edges. The word polyhedron is derived from the Greek poly (many) and the Indo-European hedron (seat).

8. All of the faces (sides) of a polyhedron are polygons.
The line segments where the faces intersect are
called edges.
The point where more than two faces intersect is
called a vertex.
vertex
edges
face

9. Some more polyhedra:

10. More polyhedron
information
Even more Polyhedron:
More polyhedron!

11. There are only five regular polyhedra called the Platonic solids.
Crystals are real world examples of polyhedra. The salt you sprinkle on your food is a crystal in the shape of a cube.
Math is everywhere!
A polyhedron is said to be regular if its faces are made up of regular polygons.
There are only five regular polyhedra called the Platonic solids.

12. More
info
In mathematics Plato's name is attached to the Platonic solids. In the Timaeus there is a mathematical construction of the elements (earth, fire, air, and water), in which the cube, tetrahedron, octahedron, and icosahedron are given as the shapes of the atoms of earth, fire, air, and water. The fifth Platonic solid, the dodecahedron, is Plato's model for the whole universe.

13. Pyramids

14. A pyramid . . . -is a polyhedron that has all faces except one
intersecting at one point;
-has one polygon base;
The sides that are not the base and intersect
in a single point are triangles.
-is named by the shape of its base.
Triangular pyramid
Pentagonal pyramid
Hexagonal pyramid

15. PRISMS

16. A prism . . . -is a polyhedron with two congruent faces called
bases that are in parallel planes.
The faces that are not bases are parallelograms,
and are called lateral faces.
-is named by the shape of its bases. E C A F B D

17. A plethora
of polyhedra

18. How in the world
do they make those?
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for more
information

19. A solid with a pair of circular bases is called a
cylinder. Is a cylinder a polyhedron?

20. A cone has a circular base and a vertex. Is a
cone a polyhedron?

21. Complete the table below.
letter
Name of polyhedron
Number of faces
Number of edges
Number of vertices A B C D E F G H

22. Completed table: A 5 9 6 B 4 C 12 8 D 7 15 10 E F 24 16 G H 21 14
letter
Name of polyhedron
Number of faces
Number of edges
Number of vertices A
Triangular prism 5 9 6 B
Triangular pyramid 4 C
Square prism 12 8 D
Pentagonal prism 7 15 10 E
Hexagonal pyramid F
Octagonal prism 24 16 G
Rectangular pyramid H
Septagonal prism 21 14
n = # sides on base
Pyramid / prism
n + 1 / n + 2
2n / 3n
n + 1 / 2n

23. What is the relationship between the number
of vertices, faces and edges in a polyhedron?
letter
Name of polyhedron
Number of faces
Number of edges
Number of vertices A
Triangular prism 5 9 6 B
Triangular pyramid 4 C
Square prism 12 8 D
Pentagonal prism 7 15 10 E
Hexagonal pyramid F
Octagonal prism 24 16 G
Rectangular pyramid H
Septagonal prism 21 14

24. More Euler information
What is the relationship between the number
of vertices, faces and edges in a polyhedron?
For any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges.
V + F = 2 + E
This is called Euler’s formula.
Click here for proofs
of Euler’s formula
More Euler information

25. Nets for many polyhedra
Interactive polyhedron
Make some polyhedron
models